Deconfined quantum criticality with internal supersymmetry

A bstract Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg-Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin SU(2), namely OSp(1|2), we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal OSp(1|2) and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including an argument for 3D XY critical behavior. Finally, we show that explicitly breaking OSp(1|2) down to SU(2) continuously connects our sDQCP to the conventional DQCP scenario.